BEIJING — In a move that has upset many in the Roman Catholic Church, the Vatican asked two “underground” bishops in China to surrender their positions to individuals approved by the country’s authoritarian government, including one the Vatican had excommunicated, a cardinal who traveled to Rome said on Monday.

The decision in December came amid what observers describe as an extraordinary effort by the Vatican to advance negotiations to restore ties with Beijing after a nearly 70-year schism among Catholics in the world’s most populous nation.

“My feeling is the Vatican wants a breakthrough,” said Dr. Chen Tsung-ming, research director at the Ferdinand Verbiest Institute in Belgium, which studies religion and society in modern China. “If they can solve, little by little, the problem of the illegal and the underground bishops, then it may help create a model of negotiations.”

Diplomatic ties between the Vatican and Beijing were severed after the Communist Party took power in China in 1949. Today, about half of the estimated 10 to 12 million Catholics in China worship in underground churches that refuse to recognize government control over the faith. The other half worship in government-managed churches run mostly by clergy members appointed by Beijing.

Restoring ties and regularizing Catholic religious life in China has been a priority for Pope Francis. Negotiations started more than 18 months ago, but they are believed to have stalled over the delicate issue of who appoints bishops in the country.

Beijing has appointed seven bishops that Rome opposes, while an estimated 30 to 40 underground bishops with Rome’s blessing operate without the Chinese government’s approval.

In a statement released on Monday, the former bishop of Hong Kong, Cardinal Joseph Zen, confirmed the broad outlines of the Vatican’s recent efforts, writing that he traveled to Rome this month to personally deliver to the pope a letter from an underground bishop who had refused to resign.

The letter came from Bishop Zhuang Jianjian of the southern Chinese city of Shantou, an 88-year-old who had been secretly ordained in 2006 with Vatican approval.

In December, Bishop Zhuang was escorted by government officials to Beijing, where he was taken to the Diaoyutai State Guesthouse to meet a papal delegation believed to have been headed by Archbishop Claudio Maria Celli, who leads the Vatican’s China negotiating team.

Bishop Zhuang had tears in his eyes when the request was made and returned to Shantou, Cardinal Zen said.

The Vatican team is said to have then traveled to Fujian Province, where it asked another underground bishop, Guo Xijin, 59, to step down. He was also asked to serve as an assistant to Zhan Silu, a government-appointed bishop whose consecration the Vatican had previously declared illegal.

In his statement on Monday, Cardinal Zen said that when he delivered Bishop Zhuang’s letter to the pope, the pontiff expressed sympathy for the underground bishops, telling the cardinal that his negotiators should not “create another Mindszenty case,” a reference to a pro-democracy bishop in Hungary who was forced out of his country in 1956 and replaced with a person acceptable to the government.

Cardinal Zen wrote that he had been heartened by the words. “I was there in the presence of the Holy Father representing my suffering brothers in China,” he said. “His words should be rightly understood as of consolation and encouragement more for them than for me.”

The Rev. Bernardo Cervellera, the editor of Asianews.it, said the developments showed that Vatican negotiators were prepared to give the Chinese government “carte blanche, and accept all requests and pose no opposition on questions that affect the church in China.”

But Father Cervellera said the pope’s reported comments to Cardinal Zen may have signaled that he was not entirely in agreement with his negotiators.

People following the issue said that the highly unusual series of events showed how badly the Vatican wanted a deal.

“The fact that both sides can carry on the negotiation till now shows that the Vatican must consider this a rare opportunity,” said Wang Meixiu, a researcher on Chinese Catholicism at the Chinese Academy of Social Sciences in Beijing.

Dr. Chen in Belgium said that one reason for the Vatican’s eagerness was a sense that the faith had been growing relatively slowly compared with other religions in China. While the number of Protestants has grown from one million in 1949 to at least 50 million today, the number of Catholics has largely tracked population growth, increasing from three million in that period to at most 12 million today, in part because of the schism in the Chinese Catholic Church.

The pope’s background as a priest in the Society of Jesus may also play a role, Dr. Chen said. Jesuits arrived in China more than 400 years ago, establishing a permanent presence for the church on the mainland after several failed efforts in earlier centuries. But they did so by being extremely flexible and conforming to local norms — a point that may be informing the pope’s negotiating approach.

“He has a sense of mission,” Dr. Chen said. “There’s a historic responsibility.”

While some have criticized the concessions — Cardinal Zen wrote in his statement on Monday that he thought “yes, definitely,” that the Vatican was “selling out the Catholic Church in China” — others say the pope has little choice.

Beijing has taken an increasingly strict line toward nongovernmental organizations, including religious groups. New religious rules are expected to go into effect on Thursday, possibly making it harder for underground churches to operate.

But the risks are also great. If Cardinal Zen’s views are shared by many Catholics, the backlash could be significant.